Sorry but there isn't a defensive system that allows the puck carrier free movement in the defensive zone 5 on 5.
There absolutely is. The idea is to NEVER chase around a player, you always want to keep them on the outside. They always want to "have their man" but the in a properly executed defensive zone strategy, players tend to stick to their coverage zones.
This is assuming the opposite team has control of the puck in the zone.
Wingers typically watch the D and the lower boards on their wing. They normally shouldn't really be going down below the goal line when the other team has control of the puck in the zone.
The D stay on their side of the ice as well. Assuming Karlsson was the one chasing Weber and Cowen is in position guarding the front of the net, Karlsson would normally stop at his goal post, the cover the front of the net and it would be up to Cowen to go towards Weber.
Although Cowen was a little slow to get to him, Andersson really dropped the ball with that slow ass lateral movement. The image posted above shows he's out of his net in the butterfly while Weber is at the goal line with his only possible shot being a backhander. Anderson should have gone back a bit and hugged the post giving him leverage to push across the crease and beat Weber to the other side with ease. It happened to him on at least another occasion.
Anyway, big deal, 2 mistakes that lead to goals. Rinne wasn't very sharp on Turris' goal either, should the Preds panic?